On the first 5 tests of her physics class, Vanessa got an average score of 84. What does she need on the next test to have an overall average of 86?
Solution: Let her score on the next test be $x$ The sum of all of her scores is then $5 \cdot 84 + x$ The same sum must also be equal to $6 \cdot 86$ Solve: $x = 6 \cdot 86 - 5 \cdot 84 = 96$.